[] add metering mode to CLI

1 files changed, 755 insertions, 0 deletions

diff --git a/contrib/libs/clapack/zlahqr.c b/contrib/libs/clapack/zlahqr.c
new file mode 100644
index 0000000000..ea4178f527
--- /dev/null
+++ b/contrib/libs/clapack/zlahqr.c
@@ -0,0 +1,755 @@
+/* zlahqr.f -- translated by f2c (version 20061008).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c__2 = 2;
+
+/* Subroutine */ int zlahqr_(logical *wantt, logical *wantz, integer *n, 
+	integer *ilo, integer *ihi, doublecomplex *h__, integer *ldh, 
+	doublecomplex *w, integer *iloz, integer *ihiz, doublecomplex *z__, 
+	integer *ldz, integer *info)
+{
+    /* System generated locals */
+    integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4;
+    doublereal d__1, d__2, d__3, d__4, d__5, d__6;
+    doublecomplex z__1, z__2, z__3, z__4, z__5, z__6, z__7;
+
+    /* Builtin functions */
+    double d_imag(doublecomplex *);
+    void d_cnjg(doublecomplex *, doublecomplex *);
+    double z_abs(doublecomplex *);
+    void z_sqrt(doublecomplex *, doublecomplex *), pow_zi(doublecomplex *, 
+	    doublecomplex *, integer *);
+
+    /* Local variables */
+    integer i__, j, k, l, m;
+    doublereal s;
+    doublecomplex t, u, v[2], x, y;
+    integer i1, i2;
+    doublecomplex t1;
+    doublereal t2;
+    doublecomplex v2;
+    doublereal aa, ab, ba, bb, h10;
+    doublecomplex h11;
+    doublereal h21;
+    doublecomplex h22, sc;
+    integer nh, nz;
+    doublereal sx;
+    integer jhi;
+    doublecomplex h11s;
+    integer jlo, its;
+    doublereal ulp;
+    doublecomplex sum;
+    doublereal tst;
+    doublecomplex temp;
+    extern /* Subroutine */ int zscal_(integer *, doublecomplex *, 
+	    doublecomplex *, integer *);
+    doublereal rtemp;
+    extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
+	    doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
+    extern doublereal dlamch_(char *);
+    doublereal safmin, safmax;
+    extern /* Subroutine */ int zlarfg_(integer *, doublecomplex *, 
+	    doublecomplex *, integer *, doublecomplex *);
+    extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *, 
+	     doublecomplex *);
+    doublereal smlnum;
+
+
+/*  -- LAPACK auxiliary routine (version 3.2) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. */
+/*     November 2006 */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*     Purpose */
+/*     ======= */
+
+/*     ZLAHQR is an auxiliary routine called by CHSEQR to update the */
+/*     eigenvalues and Schur decomposition already computed by CHSEQR, by */
+/*     dealing with the Hessenberg submatrix in rows and columns ILO to */
+/*     IHI. */
+
+/*     Arguments */
+/*     ========= */
+
+/*     WANTT   (input) LOGICAL */
+/*          = .TRUE. : the full Schur form T is required; */
+/*          = .FALSE.: only eigenvalues are required. */
+
+/*     WANTZ   (input) LOGICAL */
+/*          = .TRUE. : the matrix of Schur vectors Z is required; */
+/*          = .FALSE.: Schur vectors are not required. */
+
+/*     N       (input) INTEGER */
+/*          The order of the matrix H.  N >= 0. */
+
+/*     ILO     (input) INTEGER */
+/*     IHI     (input) INTEGER */
+/*          It is assumed that H is already upper triangular in rows and */
+/*          columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1). */
+/*          ZLAHQR works primarily with the Hessenberg submatrix in rows */
+/*          and columns ILO to IHI, but applies transformations to all of */
+/*          H if WANTT is .TRUE.. */
+/*          1 <= ILO <= max(1,IHI); IHI <= N. */
+
+/*     H       (input/output) COMPLEX*16 array, dimension (LDH,N) */
+/*          On entry, the upper Hessenberg matrix H. */
+/*          On exit, if INFO is zero and if WANTT is .TRUE., then H */
+/*          is upper triangular in rows and columns ILO:IHI.  If INFO */
+/*          is zero and if WANTT is .FALSE., then the contents of H */
+/*          are unspecified on exit.  The output state of H in case */
+/*          INF is positive is below under the description of INFO. */
+
+/*     LDH     (input) INTEGER */
+/*          The leading dimension of the array H. LDH >= max(1,N). */
+
+/*     W       (output) COMPLEX*16 array, dimension (N) */
+/*          The computed eigenvalues ILO to IHI are stored in the */
+/*          corresponding elements of W. If WANTT is .TRUE., the */
+/*          eigenvalues are stored in the same order as on the diagonal */
+/*          of the Schur form returned in H, with W(i) = H(i,i). */
+
+/*     ILOZ    (input) INTEGER */
+/*     IHIZ    (input) INTEGER */
+/*          Specify the rows of Z to which transformations must be */
+/*          applied if WANTZ is .TRUE.. */
+/*          1 <= ILOZ <= ILO; IHI <= IHIZ <= N. */
+
+/*     Z       (input/output) COMPLEX*16 array, dimension (LDZ,N) */
+/*          If WANTZ is .TRUE., on entry Z must contain the current */
+/*          matrix Z of transformations accumulated by CHSEQR, and on */
+/*          exit Z has been updated; transformations are applied only to */
+/*          the submatrix Z(ILOZ:IHIZ,ILO:IHI). */
+/*          If WANTZ is .FALSE., Z is not referenced. */
+
+/*     LDZ     (input) INTEGER */
+/*          The leading dimension of the array Z. LDZ >= max(1,N). */
+
+/*     INFO    (output) INTEGER */
+/*           =   0: successful exit */
+/*          .GT. 0: if INFO = i, ZLAHQR failed to compute all the */
+/*                  eigenvalues ILO to IHI in a total of 30 iterations */
+/*                  per eigenvalue; elements i+1:ihi of W contain */
+/*                  those eigenvalues which have been successfully */
+/*                  computed. */
+
+/*                  If INFO .GT. 0 and WANTT is .FALSE., then on exit, */
+/*                  the remaining unconverged eigenvalues are the */
+/*                  eigenvalues of the upper Hessenberg matrix */
+/*                  rows and columns ILO thorugh INFO of the final, */
+/*                  output value of H. */
+
+/*                  If INFO .GT. 0 and WANTT is .TRUE., then on exit */
+/*          (*)       (initial value of H)*U  = U*(final value of H) */
+/*                  where U is an orthognal matrix.    The final */
+/*                  value of H is upper Hessenberg and triangular in */
+/*                  rows and columns INFO+1 through IHI. */
+
+/*                  If INFO .GT. 0 and WANTZ is .TRUE., then on exit */
+/*                      (final value of Z)  = (initial value of Z)*U */
+/*                  where U is the orthogonal matrix in (*) */
+/*                  (regardless of the value of WANTT.) */
+
+/*     Further Details */
+/*     =============== */
+
+/*     02-96 Based on modifications by */
+/*     David Day, Sandia National Laboratory, USA */
+
+/*     12-04 Further modifications by */
+/*     Ralph Byers, University of Kansas, USA */
+/*     This is a modified version of ZLAHQR from LAPACK version 3.0. */
+/*     It is (1) more robust against overflow and underflow and */
+/*     (2) adopts the more conservative Ahues & Tisseur stopping */
+/*     criterion (LAWN 122, 1997). */
+
+/*     ========================================================= */
+
+/*     .. Parameters .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. Local Arrays .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Statement Functions .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Statement Function definitions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+    /* Parameter adjustments */
+    h_dim1 = *ldh;
+    h_offset = 1 + h_dim1;
+    h__ -= h_offset;
+    --w;
+    z_dim1 = *ldz;
+    z_offset = 1 + z_dim1;
+    z__ -= z_offset;
+
+    /* Function Body */
+    *info = 0;
+
+/*     Quick return if possible */
+
+    if (*n == 0) {
+	return 0;
+    }
+    if (*ilo == *ihi) {
+	i__1 = *ilo;
+	i__2 = *ilo + *ilo * h_dim1;
+	w[i__1].r = h__[i__2].r, w[i__1].i = h__[i__2].i;
+	return 0;
+    }
+
+/*     ==== clear out the trash ==== */
+    i__1 = *ihi - 3;
+    for (j = *ilo; j <= i__1; ++j) {
+	i__2 = j + 2 + j * h_dim1;
+	h__[i__2].r = 0., h__[i__2].i = 0.;
+	i__2 = j + 3 + j * h_dim1;
+	h__[i__2].r = 0., h__[i__2].i = 0.;
+/* L10: */
+    }
+    if (*ilo <= *ihi - 2) {
+	i__1 = *ihi + (*ihi - 2) * h_dim1;
+	h__[i__1].r = 0., h__[i__1].i = 0.;
+    }
+/*     ==== ensure that subdiagonal entries are real ==== */
+    if (*wantt) {
+	jlo = 1;
+	jhi = *n;
+    } else {
+	jlo = *ilo;
+	jhi = *ihi;
+    }
+    i__1 = *ihi;
+    for (i__ = *ilo + 1; i__ <= i__1; ++i__) {
+	if (d_imag(&h__[i__ + (i__ - 1) * h_dim1]) != 0.) {
+/*           ==== The following redundant normalization */
+/*           .    avoids problems with both gradual and */
+/*           .    sudden underflow in ABS(H(I,I-1)) ==== */
+	    i__2 = i__ + (i__ - 1) * h_dim1;
+	    i__3 = i__ + (i__ - 1) * h_dim1;
+	    d__3 = (d__1 = h__[i__3].r, abs(d__1)) + (d__2 = d_imag(&h__[i__ 
+		    + (i__ - 1) * h_dim1]), abs(d__2));
+	    z__1.r = h__[i__2].r / d__3, z__1.i = h__[i__2].i / d__3;
+	    sc.r = z__1.r, sc.i = z__1.i;
+	    d_cnjg(&z__2, &sc);
+	    d__1 = z_abs(&sc);
+	    z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
+	    sc.r = z__1.r, sc.i = z__1.i;
+	    i__2 = i__ + (i__ - 1) * h_dim1;
+	    d__1 = z_abs(&h__[i__ + (i__ - 1) * h_dim1]);
+	    h__[i__2].r = d__1, h__[i__2].i = 0.;
+	    i__2 = jhi - i__ + 1;
+	    zscal_(&i__2, &sc, &h__[i__ + i__ * h_dim1], ldh);
+/* Computing MIN */
+	    i__3 = jhi, i__4 = i__ + 1;
+	    i__2 = min(i__3,i__4) - jlo + 1;
+	    d_cnjg(&z__1, &sc);
+	    zscal_(&i__2, &z__1, &h__[jlo + i__ * h_dim1], &c__1);
+	    if (*wantz) {
+		i__2 = *ihiz - *iloz + 1;
+		d_cnjg(&z__1, &sc);
+		zscal_(&i__2, &z__1, &z__[*iloz + i__ * z_dim1], &c__1);
+	    }
+	}
+/* L20: */
+    }
+
+    nh = *ihi - *ilo + 1;
+    nz = *ihiz - *iloz + 1;
+
+/*     Set machine-dependent constants for the stopping criterion. */
+
+    safmin = dlamch_("SAFE MINIMUM");
+    safmax = 1. / safmin;
+    dlabad_(&safmin, &safmax);
+    ulp = dlamch_("PRECISION");
+    smlnum = safmin * ((doublereal) nh / ulp);
+
+/*     I1 and I2 are the indices of the first row and last column of H */
+/*     to which transformations must be applied. If eigenvalues only are */
+/*     being computed, I1 and I2 are set inside the main loop. */
+
+    if (*wantt) {
+	i1 = 1;
+	i2 = *n;
+    }
+
+/*     The main loop begins here. I is the loop index and decreases from */
+/*     IHI to ILO in steps of 1. Each iteration of the loop works */
+/*     with the active submatrix in rows and columns L to I. */
+/*     Eigenvalues I+1 to IHI have already converged. Either L = ILO, or */
+/*     H(L,L-1) is negligible so that the matrix splits. */
+
+    i__ = *ihi;
+L30:
+    if (i__ < *ilo) {
+	goto L150;
+    }
+
+/*     Perform QR iterations on rows and columns ILO to I until a */
+/*     submatrix of order 1 splits off at the bottom because a */
+/*     subdiagonal element has become negligible. */
+
+    l = *ilo;
+    for (its = 0; its <= 30; ++its) {
+
+/*        Look for a single small subdiagonal element. */
+
+	i__1 = l + 1;
+	for (k = i__; k >= i__1; --k) {
+	    i__2 = k + (k - 1) * h_dim1;
+	    if ((d__1 = h__[i__2].r, abs(d__1)) + (d__2 = d_imag(&h__[k + (k 
+		    - 1) * h_dim1]), abs(d__2)) <= smlnum) {
+		goto L50;
+	    }
+	    i__2 = k - 1 + (k - 1) * h_dim1;
+	    i__3 = k + k * h_dim1;
+	    tst = (d__1 = h__[i__2].r, abs(d__1)) + (d__2 = d_imag(&h__[k - 1 
+		    + (k - 1) * h_dim1]), abs(d__2)) + ((d__3 = h__[i__3].r, 
+		    abs(d__3)) + (d__4 = d_imag(&h__[k + k * h_dim1]), abs(
+		    d__4)));
+	    if (tst == 0.) {
+		if (k - 2 >= *ilo) {
+		    i__2 = k - 1 + (k - 2) * h_dim1;
+		    tst += (d__1 = h__[i__2].r, abs(d__1));
+		}
+		if (k + 1 <= *ihi) {
+		    i__2 = k + 1 + k * h_dim1;
+		    tst += (d__1 = h__[i__2].r, abs(d__1));
+		}
+	    }
+/*           ==== The following is a conservative small subdiagonal */
+/*           .    deflation criterion due to Ahues & Tisseur (LAWN 122, */
+/*           .    1997). It has better mathematical foundation and */
+/*           .    improves accuracy in some examples.  ==== */
+	    i__2 = k + (k - 1) * h_dim1;
+	    if ((d__1 = h__[i__2].r, abs(d__1)) <= ulp * tst) {
+/* Computing MAX */
+		i__2 = k + (k - 1) * h_dim1;
+		i__3 = k - 1 + k * h_dim1;
+		d__5 = (d__1 = h__[i__2].r, abs(d__1)) + (d__2 = d_imag(&h__[
+			k + (k - 1) * h_dim1]), abs(d__2)), d__6 = (d__3 = 
+			h__[i__3].r, abs(d__3)) + (d__4 = d_imag(&h__[k - 1 + 
+			k * h_dim1]), abs(d__4));
+		ab = max(d__5,d__6);
+/* Computing MIN */
+		i__2 = k + (k - 1) * h_dim1;
+		i__3 = k - 1 + k * h_dim1;
+		d__5 = (d__1 = h__[i__2].r, abs(d__1)) + (d__2 = d_imag(&h__[
+			k + (k - 1) * h_dim1]), abs(d__2)), d__6 = (d__3 = 
+			h__[i__3].r, abs(d__3)) + (d__4 = d_imag(&h__[k - 1 + 
+			k * h_dim1]), abs(d__4));
+		ba = min(d__5,d__6);
+		i__2 = k - 1 + (k - 1) * h_dim1;
+		i__3 = k + k * h_dim1;
+		z__2.r = h__[i__2].r - h__[i__3].r, z__2.i = h__[i__2].i - 
+			h__[i__3].i;
+		z__1.r = z__2.r, z__1.i = z__2.i;
+/* Computing MAX */
+		i__4 = k + k * h_dim1;
+		d__5 = (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[
+			k + k * h_dim1]), abs(d__2)), d__6 = (d__3 = z__1.r, 
+			abs(d__3)) + (d__4 = d_imag(&z__1), abs(d__4));
+		aa = max(d__5,d__6);
+		i__2 = k - 1 + (k - 1) * h_dim1;
+		i__3 = k + k * h_dim1;
+		z__2.r = h__[i__2].r - h__[i__3].r, z__2.i = h__[i__2].i - 
+			h__[i__3].i;
+		z__1.r = z__2.r, z__1.i = z__2.i;
+/* Computing MIN */
+		i__4 = k + k * h_dim1;
+		d__5 = (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[
+			k + k * h_dim1]), abs(d__2)), d__6 = (d__3 = z__1.r, 
+			abs(d__3)) + (d__4 = d_imag(&z__1), abs(d__4));
+		bb = min(d__5,d__6);
+		s = aa + ab;
+/* Computing MAX */
+		d__1 = smlnum, d__2 = ulp * (bb * (aa / s));
+		if (ba * (ab / s) <= max(d__1,d__2)) {
+		    goto L50;
+		}
+	    }
+/* L40: */
+	}
+L50:
+	l = k;
+	if (l > *ilo) {
+
+/*           H(L,L-1) is negligible */
+
+	    i__1 = l + (l - 1) * h_dim1;
+	    h__[i__1].r = 0., h__[i__1].i = 0.;
+	}
+
+/*        Exit from loop if a submatrix of order 1 has split off. */
+
+	if (l >= i__) {
+	    goto L140;
+	}
+
+/*        Now the active submatrix is in rows and columns L to I. If */
+/*        eigenvalues only are being computed, only the active submatrix */
+/*        need be transformed. */
+
+	if (! (*wantt)) {
+	    i1 = l;
+	    i2 = i__;
+	}
+
+	if (its == 10) {
+
+/*           Exceptional shift. */
+
+	    i__1 = l + 1 + l * h_dim1;
+	    s = (d__1 = h__[i__1].r, abs(d__1)) * .75;
+	    i__1 = l + l * h_dim1;
+	    z__1.r = s + h__[i__1].r, z__1.i = h__[i__1].i;
+	    t.r = z__1.r, t.i = z__1.i;
+	} else if (its == 20) {
+
+/*           Exceptional shift. */
+
+	    i__1 = i__ + (i__ - 1) * h_dim1;
+	    s = (d__1 = h__[i__1].r, abs(d__1)) * .75;
+	    i__1 = i__ + i__ * h_dim1;
+	    z__1.r = s + h__[i__1].r, z__1.i = h__[i__1].i;
+	    t.r = z__1.r, t.i = z__1.i;
+	} else {
+
+/*           Wilkinson's shift. */
+
+	    i__1 = i__ + i__ * h_dim1;
+	    t.r = h__[i__1].r, t.i = h__[i__1].i;
+	    z_sqrt(&z__2, &h__[i__ - 1 + i__ * h_dim1]);
+	    z_sqrt(&z__3, &h__[i__ + (i__ - 1) * h_dim1]);
+	    z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r * 
+		    z__3.i + z__2.i * z__3.r;
+	    u.r = z__1.r, u.i = z__1.i;
+	    s = (d__1 = u.r, abs(d__1)) + (d__2 = d_imag(&u), abs(d__2));
+	    if (s != 0.) {
+		i__1 = i__ - 1 + (i__ - 1) * h_dim1;
+		z__2.r = h__[i__1].r - t.r, z__2.i = h__[i__1].i - t.i;
+		z__1.r = z__2.r * .5, z__1.i = z__2.i * .5;
+		x.r = z__1.r, x.i = z__1.i;
+		sx = (d__1 = x.r, abs(d__1)) + (d__2 = d_imag(&x), abs(d__2));
+/* Computing MAX */
+		d__3 = s, d__4 = (d__1 = x.r, abs(d__1)) + (d__2 = d_imag(&x),
+			 abs(d__2));
+		s = max(d__3,d__4);
+		z__5.r = x.r / s, z__5.i = x.i / s;
+		pow_zi(&z__4, &z__5, &c__2);
+		z__7.r = u.r / s, z__7.i = u.i / s;
+		pow_zi(&z__6, &z__7, &c__2);
+		z__3.r = z__4.r + z__6.r, z__3.i = z__4.i + z__6.i;
+		z_sqrt(&z__2, &z__3);
+		z__1.r = s * z__2.r, z__1.i = s * z__2.i;
+		y.r = z__1.r, y.i = z__1.i;
+		if (sx > 0.) {
+		    z__1.r = x.r / sx, z__1.i = x.i / sx;
+		    z__2.r = x.r / sx, z__2.i = x.i / sx;
+		    if (z__1.r * y.r + d_imag(&z__2) * d_imag(&y) < 0.) {
+			z__3.r = -y.r, z__3.i = -y.i;
+			y.r = z__3.r, y.i = z__3.i;
+		    }
+		}
+		z__4.r = x.r + y.r, z__4.i = x.i + y.i;
+		zladiv_(&z__3, &u, &z__4);
+		z__2.r = u.r * z__3.r - u.i * z__3.i, z__2.i = u.r * z__3.i + 
+			u.i * z__3.r;
+		z__1.r = t.r - z__2.r, z__1.i = t.i - z__2.i;
+		t.r = z__1.r, t.i = z__1.i;
+	    }
+	}
+
+/*        Look for two consecutive small subdiagonal elements. */
+
+	i__1 = l + 1;
+	for (m = i__ - 1; m >= i__1; --m) {
+
+/*           Determine the effect of starting the single-shift QR */
+/*           iteration at row M, and see if this would make H(M,M-1) */
+/*           negligible. */
+
+	    i__2 = m + m * h_dim1;
+	    h11.r = h__[i__2].r, h11.i = h__[i__2].i;
+	    i__2 = m + 1 + (m + 1) * h_dim1;
+	    h22.r = h__[i__2].r, h22.i = h__[i__2].i;
+	    z__1.r = h11.r - t.r, z__1.i = h11.i - t.i;
+	    h11s.r = z__1.r, h11s.i = z__1.i;
+	    i__2 = m + 1 + m * h_dim1;
+	    h21 = h__[i__2].r;
+	    s = (d__1 = h11s.r, abs(d__1)) + (d__2 = d_imag(&h11s), abs(d__2))
+		     + abs(h21);
+	    z__1.r = h11s.r / s, z__1.i = h11s.i / s;
+	    h11s.r = z__1.r, h11s.i = z__1.i;
+	    h21 /= s;
+	    v[0].r = h11s.r, v[0].i = h11s.i;
+	    v[1].r = h21, v[1].i = 0.;
+	    i__2 = m + (m - 1) * h_dim1;
+	    h10 = h__[i__2].r;
+	    if (abs(h10) * abs(h21) <= ulp * (((d__1 = h11s.r, abs(d__1)) + (
+		    d__2 = d_imag(&h11s), abs(d__2))) * ((d__3 = h11.r, abs(
+		    d__3)) + (d__4 = d_imag(&h11), abs(d__4)) + ((d__5 = 
+		    h22.r, abs(d__5)) + (d__6 = d_imag(&h22), abs(d__6)))))) {
+		goto L70;
+	    }
+/* L60: */
+	}
+	i__1 = l + l * h_dim1;
+	h11.r = h__[i__1].r, h11.i = h__[i__1].i;
+	i__1 = l + 1 + (l + 1) * h_dim1;
+	h22.r = h__[i__1].r, h22.i = h__[i__1].i;
+	z__1.r = h11.r - t.r, z__1.i = h11.i - t.i;
+	h11s.r = z__1.r, h11s.i = z__1.i;
+	i__1 = l + 1 + l * h_dim1;
+	h21 = h__[i__1].r;
+	s = (d__1 = h11s.r, abs(d__1)) + (d__2 = d_imag(&h11s), abs(d__2)) + 
+		abs(h21);
+	z__1.r = h11s.r / s, z__1.i = h11s.i / s;
+	h11s.r = z__1.r, h11s.i = z__1.i;
+	h21 /= s;
+	v[0].r = h11s.r, v[0].i = h11s.i;
+	v[1].r = h21, v[1].i = 0.;
+L70:
+
+/*        Single-shift QR step */
+
+	i__1 = i__ - 1;
+	for (k = m; k <= i__1; ++k) {
+
+/*           The first iteration of this loop determines a reflection G */
+/*           from the vector V and applies it from left and right to H, */
+/*           thus creating a nonzero bulge below the subdiagonal. */
+
+/*           Each subsequent iteration determines a reflection G to */
+/*           restore the Hessenberg form in the (K-1)th column, and thus */
+/*           chases the bulge one step toward the bottom of the active */
+/*           submatrix. */
+
+/*           V(2) is always real before the call to ZLARFG, and hence */
+/*           after the call T2 ( = T1*V(2) ) is also real. */
+
+	    if (k > m) {
+		zcopy_(&c__2, &h__[k + (k - 1) * h_dim1], &c__1, v, &c__1);
+	    }
+	    zlarfg_(&c__2, v, &v[1], &c__1, &t1);
+	    if (k > m) {
+		i__2 = k + (k - 1) * h_dim1;
+		h__[i__2].r = v[0].r, h__[i__2].i = v[0].i;
+		i__2 = k + 1 + (k - 1) * h_dim1;
+		h__[i__2].r = 0., h__[i__2].i = 0.;
+	    }
+	    v2.r = v[1].r, v2.i = v[1].i;
+	    z__1.r = t1.r * v2.r - t1.i * v2.i, z__1.i = t1.r * v2.i + t1.i * 
+		    v2.r;
+	    t2 = z__1.r;
+
+/*           Apply G from the left to transform the rows of the matrix */
+/*           in columns K to I2. */
+
+	    i__2 = i2;
+	    for (j = k; j <= i__2; ++j) {
+		d_cnjg(&z__3, &t1);
+		i__3 = k + j * h_dim1;
+		z__2.r = z__3.r * h__[i__3].r - z__3.i * h__[i__3].i, z__2.i =
+			 z__3.r * h__[i__3].i + z__3.i * h__[i__3].r;
+		i__4 = k + 1 + j * h_dim1;
+		z__4.r = t2 * h__[i__4].r, z__4.i = t2 * h__[i__4].i;
+		z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
+		sum.r = z__1.r, sum.i = z__1.i;
+		i__3 = k + j * h_dim1;
+		i__4 = k + j * h_dim1;
+		z__1.r = h__[i__4].r - sum.r, z__1.i = h__[i__4].i - sum.i;
+		h__[i__3].r = z__1.r, h__[i__3].i = z__1.i;
+		i__3 = k + 1 + j * h_dim1;
+		i__4 = k + 1 + j * h_dim1;
+		z__2.r = sum.r * v2.r - sum.i * v2.i, z__2.i = sum.r * v2.i + 
+			sum.i * v2.r;
+		z__1.r = h__[i__4].r - z__2.r, z__1.i = h__[i__4].i - z__2.i;
+		h__[i__3].r = z__1.r, h__[i__3].i = z__1.i;
+/* L80: */
+	    }
+
+/*           Apply G from the right to transform the columns of the */
+/*           matrix in rows I1 to min(K+2,I). */
+
+/* Computing MIN */
+	    i__3 = k + 2;
+	    i__2 = min(i__3,i__);
+	    for (j = i1; j <= i__2; ++j) {
+		i__3 = j + k * h_dim1;
+		z__2.r = t1.r * h__[i__3].r - t1.i * h__[i__3].i, z__2.i = 
+			t1.r * h__[i__3].i + t1.i * h__[i__3].r;
+		i__4 = j + (k + 1) * h_dim1;
+		z__3.r = t2 * h__[i__4].r, z__3.i = t2 * h__[i__4].i;
+		z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
+		sum.r = z__1.r, sum.i = z__1.i;
+		i__3 = j + k * h_dim1;
+		i__4 = j + k * h_dim1;
+		z__1.r = h__[i__4].r - sum.r, z__1.i = h__[i__4].i - sum.i;
+		h__[i__3].r = z__1.r, h__[i__3].i = z__1.i;
+		i__3 = j + (k + 1) * h_dim1;
+		i__4 = j + (k + 1) * h_dim1;
+		d_cnjg(&z__3, &v2);
+		z__2.r = sum.r * z__3.r - sum.i * z__3.i, z__2.i = sum.r * 
+			z__3.i + sum.i * z__3.r;
+		z__1.r = h__[i__4].r - z__2.r, z__1.i = h__[i__4].i - z__2.i;
+		h__[i__3].r = z__1.r, h__[i__3].i = z__1.i;
+/* L90: */
+	    }
+
+	    if (*wantz) {
+
+/*              Accumulate transformations in the matrix Z */
+
+		i__2 = *ihiz;
+		for (j = *iloz; j <= i__2; ++j) {
+		    i__3 = j + k * z_dim1;
+		    z__2.r = t1.r * z__[i__3].r - t1.i * z__[i__3].i, z__2.i =
+			     t1.r * z__[i__3].i + t1.i * z__[i__3].r;
+		    i__4 = j + (k + 1) * z_dim1;
+		    z__3.r = t2 * z__[i__4].r, z__3.i = t2 * z__[i__4].i;
+		    z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
+		    sum.r = z__1.r, sum.i = z__1.i;
+		    i__3 = j + k * z_dim1;
+		    i__4 = j + k * z_dim1;
+		    z__1.r = z__[i__4].r - sum.r, z__1.i = z__[i__4].i - 
+			    sum.i;
+		    z__[i__3].r = z__1.r, z__[i__3].i = z__1.i;
+		    i__3 = j + (k + 1) * z_dim1;
+		    i__4 = j + (k + 1) * z_dim1;
+		    d_cnjg(&z__3, &v2);
+		    z__2.r = sum.r * z__3.r - sum.i * z__3.i, z__2.i = sum.r *
+			     z__3.i + sum.i * z__3.r;
+		    z__1.r = z__[i__4].r - z__2.r, z__1.i = z__[i__4].i - 
+			    z__2.i;
+		    z__[i__3].r = z__1.r, z__[i__3].i = z__1.i;
+/* L100: */
+		}
+	    }
+
+	    if (k == m && m > l) {
+
+/*              If the QR step was started at row M > L because two */
+/*              consecutive small subdiagonals were found, then extra */
+/*              scaling must be performed to ensure that H(M,M-1) remains */
+/*              real. */
+
+		z__1.r = 1. - t1.r, z__1.i = 0. - t1.i;
+		temp.r = z__1.r, temp.i = z__1.i;
+		d__1 = z_abs(&temp);
+		z__1.r = temp.r / d__1, z__1.i = temp.i / d__1;
+		temp.r = z__1.r, temp.i = z__1.i;
+		i__2 = m + 1 + m * h_dim1;
+		i__3 = m + 1 + m * h_dim1;
+		d_cnjg(&z__2, &temp);
+		z__1.r = h__[i__3].r * z__2.r - h__[i__3].i * z__2.i, z__1.i =
+			 h__[i__3].r * z__2.i + h__[i__3].i * z__2.r;
+		h__[i__2].r = z__1.r, h__[i__2].i = z__1.i;
+		if (m + 2 <= i__) {
+		    i__2 = m + 2 + (m + 1) * h_dim1;
+		    i__3 = m + 2 + (m + 1) * h_dim1;
+		    z__1.r = h__[i__3].r * temp.r - h__[i__3].i * temp.i, 
+			    z__1.i = h__[i__3].r * temp.i + h__[i__3].i * 
+			    temp.r;
+		    h__[i__2].r = z__1.r, h__[i__2].i = z__1.i;
+		}
+		i__2 = i__;
+		for (j = m; j <= i__2; ++j) {
+		    if (j != m + 1) {
+			if (i2 > j) {
+			    i__3 = i2 - j;
+			    zscal_(&i__3, &temp, &h__[j + (j + 1) * h_dim1], 
+				    ldh);
+			}
+			i__3 = j - i1;
+			d_cnjg(&z__1, &temp);
+			zscal_(&i__3, &z__1, &h__[i1 + j * h_dim1], &c__1);
+			if (*wantz) {
+			    d_cnjg(&z__1, &temp);
+			    zscal_(&nz, &z__1, &z__[*iloz + j * z_dim1], &
+				    c__1);
+			}
+		    }
+/* L110: */
+		}
+	    }
+/* L120: */
+	}
+
+/*        Ensure that H(I,I-1) is real. */
+
+	i__1 = i__ + (i__ - 1) * h_dim1;
+	temp.r = h__[i__1].r, temp.i = h__[i__1].i;
+	if (d_imag(&temp) != 0.) {
+	    rtemp = z_abs(&temp);
+	    i__1 = i__ + (i__ - 1) * h_dim1;
+	    h__[i__1].r = rtemp, h__[i__1].i = 0.;
+	    z__1.r = temp.r / rtemp, z__1.i = temp.i / rtemp;
+	    temp.r = z__1.r, temp.i = z__1.i;
+	    if (i2 > i__) {
+		i__1 = i2 - i__;
+		d_cnjg(&z__1, &temp);
+		zscal_(&i__1, &z__1, &h__[i__ + (i__ + 1) * h_dim1], ldh);
+	    }
+	    i__1 = i__ - i1;
+	    zscal_(&i__1, &temp, &h__[i1 + i__ * h_dim1], &c__1);
+	    if (*wantz) {
+		zscal_(&nz, &temp, &z__[*iloz + i__ * z_dim1], &c__1);
+	    }
+	}
+
+/* L130: */
+    }
+
+/*     Failure to converge in remaining number of iterations */
+
+    *info = i__;
+    return 0;
+
+L140:
+
+/*     H(I,I-1) is negligible: one eigenvalue has converged. */
+
+    i__1 = i__;
+    i__2 = i__ + i__ * h_dim1;
+    w[i__1].r = h__[i__2].r, w[i__1].i = h__[i__2].i;
+
+/*     return to start of the main loop with new value of I. */
+
+    i__ = l - 1;
+    goto L30;
+
+L150:
+    return 0;
+
+/*     End of ZLAHQR */
+
+} /* zlahqr_ */